{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:11:54Z","timestamp":1760148714105,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T00:00:00Z","timestamp":1685059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we investigate the generalized Kawahara\u2013KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two non-negative classical solutions. The arguments are based upon recent theoretical results.<\/jats:p>","DOI":"10.3390\/sym15061159","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T16:10:53Z","timestamp":1685203853000},"page":"1159","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Classical Solutions for the Generalized Kawahara\u2013KdV System"],"prefix":"10.3390","volume":"15","author":[{"given":"Svetlin G.","family":"Georgiev","sequence":"first","affiliation":[{"name":"Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, 1164 Sofia, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8586-1058","authenticated-orcid":false,"given":"A.","family":"Boukarou","sequence":"additional","affiliation":[{"name":"Dynamic Systems Laboratory, Faculty of Mathematics, University of Science and Technology Houari Boumediene, Bab Ezzouar 16000, Algeria"}]},{"given":"Keltoum","family":"Bouhali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51452, Saudi Arabia"},{"name":"D\u00e9partement des Math\u00e9matiqus, Universit\u00e9 20 Ao\u00fbt 1955 Skikda Bp 26 Route El-Hadaiek, Skikda 21000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7895-4168","authenticated-orcid":false,"given":"Khaled","family":"Zennir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51452, Saudi Arabia"}]},{"given":"Hatim M.","family":"Elkhair","sequence":"additional","affiliation":[{"name":"Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University, P.O. Box 5701, Riyadh 11432, Saudi Arabia"}]},{"given":"Eltegani I.","family":"Hassan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}]},{"given":"Alnadhief H. A.","family":"Alfedeel","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}]},{"given":"Almonther","family":"Alarfaj","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2985","DOI":"10.1007\/s00245-020-09737-5","article-title":"Well-Posedness for a Coupled System of Kawahara\/KdV Type Equations","volume":"84","author":"Kondo","year":"2021","journal-title":"Appl. Math. Optim."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Boukarou, A., Guerbati, K., Zennir, K., Alodhaibi, S., and Alkhalaf, S. (2020). 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Equ."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Shah, N.A., Hamed, Y.S., Abualnaja, K.M., Chung, J.-D., and Khan, A. (2022). A Comparative Analysis of Fractional-Order Kaup-Kupershmidt Equation within Different Operators. Symmetry, 14.","DOI":"10.3390\/sym14050986"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Shah, N.A., Alyousef, H.A., El-Tantawy, S.A., and Chung, J.D. (2022). Analytical Investigation of Fractional-Order Korteweg\u2014De-Vries-Type Equations under Atangana-Baleanu-Caputo Operator: Modeling Nonlinear Waves in a Plasma and Fluid. Symmetry, 14.","DOI":"10.3390\/sym14040739"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Shah, N.A., Agarwal, P., Chung, J.D., El-Zahar, E.R., and Hamed, Y.S. (2020). Analysis of Optical Solitons for Nonlinear Schr\u00f6dinger Equation with Detuning Term by Iterative Transform Method. Symmetry, 12.","DOI":"10.3390\/sym12111850"},{"key":"ref_9","unstructured":"Banas, J., and Goebel, K. (1980). 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Handbook of Integral Equations, CRC Press.","DOI":"10.1201\/9781420050066"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/6\/1159\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:42:54Z","timestamp":1760125374000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/6\/1159"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,26]]},"references-count":12,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["sym15061159"],"URL":"https:\/\/doi.org\/10.3390\/sym15061159","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,5,26]]}}}